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This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.
- Sales Rank: #218916 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2009-04-20
- Original language: English
- Number of items: 1
- Dimensions: 9.96" h x 1.38" w x 8.46" l, 2.65 pounds
- Binding: Hardcover
- 594 pages
- Used Book in Good Condition
Review
"This text is a major achievement that brings together all of the important developments in complexity theory. Student and researchers alike will find it to be an immensely useful resource."
Michael Sipser, MIT, author of Introduction to the Theory of Computation
"Computational complexity theory is at the core of theoretical computer science research. This book contains essentially all of the (many) exciting developments of the last two decades, with high level intuition and detailed technical proofs. It is a must for everyone interested in this field."
Avi Wigderson, Professor, Institute for Advanced Study, Princeton
"This book by two leading theoretical computer scientists provides a comprehensive,insightful and mathematically precise overview of computational complexity theory, ranging from early foundational work to emerging areas such as quantum computation and hardness of approximation. It will serve the needs of a wide audience, ranging from experienced researchers to graduate students and ambitious undergraduates seeking an introduction to the mathematical foundations of computer science. I will keep it at my side as a useful reference for my own teaching and research."
Richard M. Karp, University Professor, University of California at Berkeley
"The reviewer's impressions are that this new textbook on computational complexity is available for a very attractive price and that on Amazon it may be verified that it has received very good reviews by several leaders in this field (Karp, Sipser, Wigderson)."
Ulrich Tamm, Mathematical Reviews
About the Author
Sanjeev Arora is a Professor in the department of computer science at Princeton University. He holds a Ph.D. from the University of California, Berkeley and has done foundational work in complexity theory, probabilistically checkable proofs, and approximation algorithms.
Boaz Barak is an assistant professor in the department of computer science at Princeton University. He holds a Ph.D. from the Weizmann Institute of Science.
Most helpful customer reviews
42 of 43 people found the following review helpful.
Mixed feelings about this book
By NULL VOID
I own two copies of this book: a hardcopy I keep at home, and the PDF version on my Nook (which I bought directly from the publisher). I'm happy that there is an eBook version given that I often run or bike to school and don't have to lug this thing around with me.
That said, I'm not crazy about this book. It is the required text for our graduate complexity theory course. I've found with some regularity that I did not really understand the assigned chapters until I attended the professor's lectures and read his slides in detail. It really seems to be geared toward presenting the most recent results in complexity theory in textbook form. I personally think it would be better suited to an advanced complexity theory course.
Contrast this with Papadimitriou's "Computational Complexity" (1993) which is a little out of date, but WOW, is it readable. Reductions, which are the bread and butter of complexity theorists get an entire chapter in Papadimitriou whereas they get a few pages in AB. Also, Papadimitriou's style is much more conversational, and he points out pitfalls and other considerations that novice mathematicians would simply miss. Oh, and Papadimitriou uses the word "trivial" sparingly, unlike AB, who sprinkle it liberally throughout their text. "Trivially"? Oh REALLY? For WHOM?!! Sorry, kind of a pet peeve of mine.
Were I a student engaging in self-study, I would obviously choose Papadimitriou despite the fact that it's a bit more expensive. It already seems like an old friend to me. I'll probably keep AB around as a reference, but it is definitely not my go-to book.
30 of 32 people found the following review helpful.
Frustrating: Kindle Edition Needs Major Revisions
By write(eval(read(.))
I know this book is one of the best complexity book, but its Kindle Edition is the worst.
Because it is unreadable at all.
It is unable to display some important mathematical fonts (e.g. epsilon for sets, floor/ceil brackets, ...), I saw several white squares of my screen per page. Conversion (with OCR or something?) runs without accuracy, so we found two or more "glued" words (e.g. bytheway,...) per screen. I have informed each that sort of "typos" this couple of days, yes, that was a exhaustive (and un-payed) job. No, I won't do this sort of volunteer any more. So I wrote this.
The kindle edition of this book, or any other Math/Sci books likely to give seriously bad impressions not only to the originals (and authors who approved to Kindle it,) but the poor expressive capability of Kindle itself.
Please drop every suspicious kindle editions from your product list right now, and please improve accuracy of making of kindle edition.
And, if you think books are things that to be read, please revise current unreadable edition and republish it.
Why kindle edition has no "refund" or "replace kindle edition with hardcopy edition" options?
42 of 49 people found the following review helpful.
So far SO good!
By Nicholas Sterling
I almost didn't order this book. I had visions of opening the box and pulling out some incomprehensible tome with one coma-inducing proof after another. I have a BS in math, but that was an embarrassingly long time ago, so I wasn't sure I was up for a real test of my sanity. What a relief it was to see that this book is relatively approachable.
OK, wait -- quick sanity check. This *is* a textbook about the mathematical analysis of computation; hopefully you wouldn't even be reading this review if you couldn't wade through a jungle of mathematical proofs, if you didn't know some discrete math, graph theory, etc., or if you didn't have some programming experience. There are formal notations everywhere. The subject matter of this book sets a pretty high bar, regardless of how the book is written.
So, back to how the book is written. Very well! Yes, there are proofs and lemmas everywhere, but the authors do several things to focus on getting the point across without being tiresome. First, they are great about motivating what they are talking about. Why is this issue important? Why are we going to approach the problem this way? Second, they are generous with well thought out diagrams that depict what is being described in words. A few good diagrams go a long way with me, personally. Third, in some cases they just give "hand-wavy proofs." By not getting hung up the formality of the proofs, they can choose interesting statements to prove and get the idea across in a paragraph. May I just say "Hallelujah!" -- I wish more books took this approach, concentrating more on understanding than on formality. Fourth, they sometimes take two runs at a proof, once just talking their way through it, saying what is going to happen, and then going back over it a second time formally. Fifth, they have quite interesting "chapter notes" that give interesting history about how a topic developed over the years and how it has been important in the "real world." The book is also very well typeset -- easy on the eye.
I was delighted to see a section on cryptography followed by a section on quantum computing, which has huge implications for cryptography precisely because of what it means for computational complexity (of integer factorization, in particular). The section "Shor's ideas in nutshell" is a perfect example of how the authors took something that could have been quite tedious and talked the (prepared) reader through it in a way that is not only comprehensible but interesting.
This is not to say that the book is not rigorous. But rigorous doesn't have to be tedious.
I will try to update this later as I read further, but so far, I'm quite impressed. This book assumes you have some serious background, but then treats you kindly.
Oh, and the price -- it's less than half what I would have expected a book like this to cost. I thought I was reviewing the wrong book for a minute! :^) Kudos to Cambridge University Press for keeping prices down.
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